1. Field of the Invention
The present invention is related to a catadioptric optical element, in particular a catadioptric lens, and to an optical system that includes the catadioptric optical element.
2. Description of the Related Art
Imaging apparatuses, such as a microscope, a lithographic projection system, or even a telescope, use purely reflective (catoptric), purely refractive (dioptric), or a combination of reflective and refractive (catadioptric) optical elements to image a specimen. A microscope uses an objective optical system to observe a sample, such as a biological tissue, a defect on a semiconductor wafer or a surface of material. A lithographic projection system uses a projection objective to project an image of a pattern on a reticle onto a planar image surface of a semiconductor substrate (wafer). In a telescope, an objective lens, larger in diameter than the pupil of a human eye, permits the collection of enough light to make visible distant point sources such as stars that otherwise may not be observed. To produce a good image, these instruments must collect enough light reflected from (or transmitted through) an object, separate the details in the image, magnify the image, and render the details visible to the human eye or an optical detector.
The ability to resolve fine object details at a fixed object distance, regardless of whether the details correspond to physically close features (as in a microscope) or to features separated by a small angle (as in a telescope), is determined by the instrument's resolution. Resolution (R) of a microscope is given by Equation (1).
                    R        =                  0.61          ×                      λ            NA                                              (        1        )            
Where λ is the wavelength of the light used, NA is the numerical aperture of the microscope on an object space, and 0.61 is derived from the Rayleigh criterion.
As it is known to those skilled in the art, the larger NA of the microscope is, the better the resolution is. Accordingly, from the above requirements of Equation (1), the minimum resolvable separation of two object points can be reduced (resolution improved) by increasing the lens diameter and decreasing the wavelength used. Hence, the advantage of using ultraviolet (UV), deep ultraviolet (DUV), X-ray, and electron microscopes (or projection objectives) for high-resolution applications.
On the other hand, NA is also determined by the instruments' ability to gather enough light to resolve fine object details. In terms of its ability to gather enough light, the NA of a microscope is defined by Equation (2), as follows.NA=No sin θm  (2)
Where θm is the angle of marginal ray that comes from the object and No is the refractive index of the object space. From the perspective of Equation (2), therefore, in order to obtain high NA, the marginal ray θm needs to be large. However, this results in more difficulty for correcting aberrations. On the other hand, increasing the refractive index of object space can also make NA larger. However, when air (No=1) is used in the object space, the maximum value of NA cannot be greater than unity, but when the object space is filled with a fluid of index larger than 1 (No>1) a NA larger than 1 can be achieved. Accordingly, most conventional microscopes use objectives with NA values in the approximate range of 0.08 to 1.30, with the proviso that NA values greater than 0.95 can typically be achieved only by using an immersion fluid in the object space.
Many designs for high NA objectives use a catadioptric system, which includes both refractive and reflective components. In particular, projection objectives for immersion lithography use a catadioptric optical element as a last optical element which serves as a field correcting optic to increase the NA value. See, for example, U.S. Pat. No. 5,650,877 and International Publication Number WO2008/101676 by Aurelian Dodoc (herein “WO2008/101676”).
In U.S. Pat. No. 5,650,877, a reducing optical element having specially configured front and back faces projects a reduced image of the reticle onto a substrate. The back face of the reducing optical element has a central aperture surrounded by a concave reflective surface. The front face has a partially reflective surface that transmits a portion of the light beam toward the concave reflecting surface and reflects a portion of the remaining light beam returned by the concave reflective surface on a converging path through the central aperture. The substrate is aligned with the aperture.
WO2008/101676 discloses a catadioptric optical element made of a high-index transparent material having a first surface on an object-side of the element and a second surface opposite to the first surface. The second surface has a transmissive portion in a central region around the optical axis and a concave reflective portion in a zone around the transmissive portion. The first surface has a transmissive zone to transmit radiation coming from the object surface towards the second surface and oriented relative to the second surface such that at least a portion of radiation reflected by the reflective portion of the second surface is totally reflected by the transmissive portion of the first surface towards the transmissive portion of the second surface.
In addition, Grey et al., in an article entitled “A New Series of Microscope Objective: I. Catadioptric Newtonian Systems,” JOSA 39, No 9, 719-723 (1949), discloses a microscope objective with a last solid lens made of fluorite or quartz-fluorite, where both object-side and image-side surfaces of the lens contain reflective coating on certain regions thereof to achieve NA values greater than 0.95 at 220 to 540 nm wavelengths with negligible aberrations.
One feature common to each of the above discussed references is that a central obscuration blocks a portion of the light from passing through the central region of the objective's catadioptric optical element. The central obscuration beyond a certain threshold (typically 25%) can cause significant degradation in image contrast and loss of light intensity. According to U.S. Pat. No. 5,650,877, the central obscuration may be limited in size to block no more than 15 percent of the projected image. However, although obscuration is relatively low, substantial energy loss is caused by partial reflection.
In the catadioptric optical element of WO2008/101676, total internal reflection (TIR) is used to increase the NA. To properly visualize the physical conditions for total internal reflection, FIG. 1 illustrates the geometry of rays refracted at a plane interface of a first medium of refractive index n1 and a second medium of refractive index n2. Referring to FIG. 1, consider a light ray R1 originating at an object point O and having an incidence angle θ1 incident on a plane interface S between the first medium of refractive index n1 and the second medium of refractive index n2. Upon transmitting through the first medium of refractive index n1 to the second medium of refractive index n2, the light ray R1 will be refracted as a light ray R1′ at an angle of refraction θ2, in accordance with Snell's law.
Snell's law, which takes the form, n1 sin θ1=n2 sin θ2, requires an angle of refraction θ2 such that the refracted ray R1′ bends away from the normal Nr when n1>n2 (as illustrated in FIG. 1), or the refracted ray bends towards the normal when n2>n1 (not illustrated). Snell's law also requires that a ray R0 having an incidence angle θ1=0 (i.e., incident perpendicular or normal) to the interface S be transmitted without change in direction, regardless of the ratio of refractive indices. As illustrated in FIG. 1, rays R1 and R2 that make increasingly larger angles of incidence θ1 with respect to the normal Nr must, by Snell's law, refract at increasingly larger angles θ2 as refracted rays R1′ and R2′, respectively.
A critical angle of incidence θc is reached when a ray R3 is incident on the interface S at this critical angle θc. In this case, the light ray is refracted as ray R3′ at an angle of refraction that reaches 90 degrees with respect to the normal Nr. Thus, from Snell's law, when θ2=90°, the critical angle θc=arcsin (n2/n1). Accordingly, it holds that for angles of incidence greater than θc, the incident ray R4 is not refracted, but it is instead reflected as R4′ because it experiences total internal reflection (TIR).
In consideration of the above premise, total internal reflection of light rays occurs between a lens and air, if Snell's law conditions are satisfied for the critical angle θc given by Equation (3).
                              θ          c                =                  arcsin          ⁡                      (                          1              N                        )                                              (        3        )            
where N is the refractive index of the lens, and 1 is the assumed refractive index of air.
Referring now to FIG. 2, relevant portions of a catadioptric lens disclosed by WO2008/101676 are discussed. In FIG. 2, a side view of a catadioptric lens 100, which has a first surface 101 and a second surface 102 opposite to each other, is illustrated on the left side of the drawing. The first surface 101 is generally concave when seen from the side of the second surface 102, and the second surface 102 is substantially planar (flat). A front view of the substantially planar second surface 102 is illustrated on the right side of FIG. 2. The first surface 101 has a transmissive portion in a central region around the optical axis AX and a concave reflective portion in a region around the transmissive portion. The second surface 102 is generally transparent and has a total internal reflection (TIR) region 106 and transmissive region 107, which are concentric to each other and also centered on the optical axis AX. Light illuminating an object O passes through the transmissive portion of the first surface 101 and impinges first on the second surface 102. More specifically, light rays R1 and R2 having angles of incidence between the critical angle θc and the marginal angle θm undergo total internal reflection on the TIR region 106 of the second surface 102, and are therefore reflected towards the reflective portion of the first surface 101. In turn, the reflective portion of the first surface 101 reflects these rays back towards the second surface 102 as light rays R1′ and R2′. This time, however, since the incident angles of rays R1′ and R2′ are less than the critical angle, the rays R1′ and R2′ are transmitted through the TIR region 106 of the second surface 102.
On the other hand, a light ray R0 propagating through the transmissive region of the first surface 101 and impinging on the transmissive region 107 of the second surface 102, with an incident angle θl less than the critical angle θc, cannot be reflected by the second surface 102, but instead is refracted as a light ray R0′. The refracted ray R0′ may be scattered or blocked by a central obscuration or field stop aperture; thus, light rays R0 with an incident angle θl less than the critical angle θc do not contribute to image formation. Moreover, the transmissive region 107 immediately around the optical axis AX is obscured because the object itself blocks light incident normal to the object. The region 107, therefore, may degrade image contrast and cause loss of energy of the light.
Generally, an obscuration ratio, which shows how much illumination light rays are lost in a high NA system, is defined by the Equation (4).
                    Obscuration        =                              sin            ⁢                                                  ⁢                          θ              l                                            sin            ⁢                                                  ⁢                          θ              m                                                          (        4        )            
where θl is the lowest angle to achieve the required obscuration ratio. The rays R0 below the critical angle θc which reach the region 107 in FIG. 2 are not reflected but refracted which is not desirable. In WO 2008/101676, therefore, obscuration is given by Equation (5), as shown below:
                    Obscuration        =                              sin            ⁢                          {                              arcsin                ⁡                                  (                                      1                    N                                    )                                            }                                            sin            ⁢                                                  ⁢                          θ              m                                                          (        5        )            
Therefore, since θl is smaller than the critical angle θc, it means that the requirement for obscuration may not be satisfied.
Accordingly, there is a need to improve on the current state of the art, so that catadioptric optical systems may provide the highest possible numerical aperture with the lowest obscuration ratio, without sacrificing image quality.